There is a pair of vertical angles whose measures are m∠1=106°

Question

and m∠2=(3x−75)°
. What equation can you write to solve for x
?(1 point)
Responses

3x°−75°+106°=180°
3 x minus 75 plus 106 degrees equals 180 degrees

3x°−75°=106°
3 x minus 75 equals 106 degrees

3x°−75°+106°=90°
3 x minus 75 plus 106 degrees equals 90 degrees

3x°−75°−106°=180°

Answer 1

Since angles 1 and 2 are vertical angles, they are equal. Therefore, you can set their measures equal to each other. Given that:

• \( m∠1 = 106° \)
• \( m∠2 = (3x - 75)° \)

You can write the equation as:

\[ 106° = (3x - 75)° \]

To isolate \( x \), you could rearrange it. However, from the provided options, the most straightforward related equation that leads towards solving for \( x \) is:

\[ 3x° - 75° = 106° \]

This is the second response option.